Math Problem Statement

Find dy/dx by implicit differentiation. tan^(−1)(3x^2y) = x + 5xy^2

Solution

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Math Problem Analysis

Mathematical Concepts

Implicit Differentiation
Inverse Trigonometric Functions
Chain Rule

Formulas

d/dx[tan^(-1)(u)] = 1 / (1 + u^2) * du/dx
Chain Rule: d/dx[f(g(x))] = f'(g(x)) * g'(x)

Theorems

Chain Rule for Differentiation
Derivative of Inverse Trigonometric Functions

Suitable Grade Level

Undergraduate Calculus